Mary

A ski lift has a one-way length of 1 km and a vertical rise of 200 m. The chairs are spaced 20 m apart (assume 49 chairs), and each one weighs 300 kg with three occupants. The lift is operating at a steady speed of 10 km/h. Neglecting friction and air drag, determine the power required to steadily operate this ski lift.

A rocket of mass m traveling with speed y0 along the x axis suddenly shoots out fuel equal

to one-third its mass, perpendicular to the x axis (along the y axis) with speed 2y0 * Express

the final velocity of the rocket in i, j, k notation.

I'm not sure how to begin this problem. I drew a diagram of the scenario, but I'm not sure if the rocket is supposed to shoot directly up, or at an angle. Even with that information, I'm still confused.

Long John Silver, a pirate, has buried his treasure on an island with five trees located at the following points: A (30.0 m, -20.0 m), B (60.0 m, 80.0 m), C (-10.0 m, -10.0 m), D (40.0 m, -30.0 m), and E (-70.0 m, 60.0 m). All of the points are measured relative to some origin, as in Figure P3.21. Long John's map instructs you to start at A and move toward B, but cover only one-third the distance between A and B. then move toward C, covering one-fourth the distance between your current location and C. Then move toward D, covering one-fourth the distance between where you are and D. Finally, move toward E, covering one-fourth the distance between you and E, stop, and dig.

http://www.webassign.net/sercp/p3-21.gif

(a) What are the coordinates of the point where the pirate's treasure is buried?

I don't know if I started this right, but for the first distance traveled, I got a vector of 34.8 starting from A to a third of the way to B. From that point to a fourth of the way to C, I got a vector of 13.79. I started to get things jumbled from there and now I'm just stuck.

We've haven't done anything similar to this in class so I don't really know where to start. I'm confused as to what my teacher is looking for:

A projectile is fired with an initial speed of v0 at an angle of θ0 to the horizontal, as in Figure 3.14. When it reaches its peak, it has (x, y) coordinates given by (R/2, h), and when it strikes the ground, its coordinates are (R, 0), where R is called the horizontal range.

Figure 3.14 : http://www.webassign.net/sercp/3-14.gif

(a) Show that it reaches a maximum height, h, given by the following equation.

h= (Vo^2sin^2(theta)o)/2g

(b) Show that its horizontal range is given by the following equation.

R= (Vo^2sin2(theta)o)/g

An ice sled powered by a rocket engine starts from rest on a large frozen lake and accelerates at +38 ft/s2. After some time t1, the rocket engine is shut down and the sled moves with constant velocity v for a time t2. Assume the total distance traveled by the sled is 15750 ft and the total time is 90 s.

(a) Find the times t1 and t2.

t1 s

t2 s

(b) Find the velocity v.

ft/s

At the 15750 ft mark, the sled begins to accelerate at -21 ft/s2.

(c) What is the final position of the sled when it comes to rest?

ft

(d) What is the duration of the entire trip?

A certain cable car in San Francisco can stop in 10 s when traveling at maximum speed. On one occasion, the driver sees a dog a distance d m in front of the car and slams on the brakes instantly. The car reaches the dog 7.44 s later, and the dog jumps off the track just in time. If the car travels 3.67 m beyond the position of the dog before coming to a stop, how far was the car from the dog? [Hint: You will need three equations.]